Goran Konjevod

Linear-programming-based techniques for synthesis of network-on-chip architectures

Network-on-chip (NoC) has been proposed as a solution for the communication challenges of system-on-chip (SoC) design in the nanoscale regime. SoC design offers the opportunity for incorporating custom NoC architectures that are more suitable for a particular application, and do not necessarily conform to regular topologies. This paper presents novel linear programming based techniques for synthesis of custom NoC architectures. In the nanoscale regime, low power consumption would continue to be an important design goal. We first discuss an optimal mixed integer linear programming (MILP) formulation that synthesizes a low power NoC architecture subject to the performance constraints. The MILP formulation is limited by large run times. We next present heuristic techniques that exploit clustering, and 0-1 constraint relaxation to reduce the run times of the formulation. The techniques minimize power as the primary goal, and minimize the number of routers (area) as a secondary goal. We present an analysis of the quality of the results and the solution times of the proposed techniques by extensive experimentation with the realistic benchmarks. The clustering based heuristic generates results whose power consumption is within 11% of the MILP solutions and its average run time is 171.1 seconds. The average run time of the relaxation and rounding based techniques is less than 2 seconds, and the power consumption of their solutions is within 58% of the MILP result.

A Polylogarithmic Approximation Algorithm for the Group Steiner Tree Problem

Given a weighted graph with some subsets of vertices called groups, the group Steiner tree problem is to find a minimum-weight subgraph which contains at least one vertex from each group. We give a randomized algorithm with a polylogarithmic approximation guarantee for the group Steiner tree problem. The previous best approximation guarantee was O(i 2 k 1/i ) in time O(n i k 2i ) (Charikar, Chekuri, Goel, and Guha). Our algorithm also improves existing approximation results for network design problems with location-based constraints and for the symmetric generalized traveling salesman problem.

An automated technique for topology and route generation of application specific on-chip interconnection networks

Network-on-chip (NoC) has been proposed as a solution to the communication challenges of system-on-chip (SoC) design in nanoscale technologies. Application specific SoC design offers the opportunity for incorporating custom NoC architectures that are more suitable for a particular application, and do not necessarily conform to regular topologies. Custom NoC design in nanoscale technologies must address performance requirements, power consumption and physical layout considerations. This paper presents a novel three phase technique that i) generates a performance aware layout of the SoC, ii) maps the cores of the SoC to routers, and iii) generates a unique route for every trace that satisfies the performance and architectural constraints. We present an analysis of the quality of the results of the proposed technique by experimentation with realistic benchmarks.

Linear programming based techniques for synthesis of network-on-chip architectures

Application-specific system-on-chip (SoC) design offers the opportunity for incorporating custom network-on-chip (NoC) architectures that are more suitable for a particular application, and do not necessarily conform to regular topologies. This paper presents novel mixed integer linear programming (MILP) formulations for synthesis of custom NoC architectures. The optimization objective of the techniques is to minimize the power consumption subject to the performance constraints. We present a two-stage approach for solving the custom NoC synthesis problem. The power consumption of the NoC architecture is determined by both the physical links and routers. The power consumption of a physical link is dependent upon the length of the link, which in turn, is governed by the layout of the SoC. Therefore, in the first stage, we address the floorplanning problem that determines the locations of the various cores and the routers. In the second stage, we utilize the floorplan from the first stage to generate topology of the NoC and the routes for the various traffic traces. We also present a clustering-based heuristic technique for the second stage to reduce the run times of the MILP formulation. We analyze the quality of the results and solution times of the proposed techniques by extensive experimentation with realistic benchmarks and comparisons with regular mesh-based NoC architectures.

On the establishment of distinct identities in overlay networks

We study ways to restrict or prevent the damage that can be caused in a peer-to-peer network by corrupt entities creating multiple pseudonyms. We show that it is possible to remotely issue certificates that can be used to test the distinctness of identities. To our knowledge, this is the first work that shows that remote anonymous certification of identity is possible under adversarial conditions. Our certification protocols are based on geometric techniques that establish location information in a fault-tolerant and distributed fashion. They do not rely on a centralized certifying authority or infrastructure that has direct knowledge of entities in the system, and work in Euclidean or spherical geometry of arbitrary dimension. Our protocols tolerate corrupt entities, including corrupt certifiers as well as collusion by certification applicants and certifiers. We consider both broadcast and point-to-point message passing models.

Origami based Mechanical Metamaterials

We describe mechanical metamaterials created by folding flat sheets in the tradition of origami, the art of paper folding, and study them in terms of their basic geometric and stiffness properties, as well as load bearing capability. A periodic Miura-ori pattern and a non-periodic Ron Resch pattern were studied. Unexceptional coexistence of positive and negative Poissons ratio was reported for Miura-ori pattern, which are consistent with the interesting shear behavior and infinity bulk modulus of the same pattern. Unusually strong load bearing capability of the Ron Resch pattern was found and attributed to the unique way of folding. This work paves the way to the study of intriguing properties of origami structures as mechanical metamaterials.

Robust optimization of contaminant sensor placement for community water systems

We present a series of related robust optimization models for placing sensors in municipal water networks to detect contaminants that are maliciously or accidentally injected. We formulate sensor placement problems as mixed-integer programs, for which the objective coefficients are not known with certainty. We consider a restricted absolute robustness criteria that is motivated by natural restrictions on the uncertain data, and we define three robust optimization models that differ in how the coefficients in the objective vary. Under one set of assumptions there exists a sensor placement that is optimal for all admissible realizations of the coefficients. Under other assumptions, we can apply sorting to solve each worst-case realization efficiently, or we can apply duality to integrate the worst-case outcome and have one integer program. The most difficult case is where the objective parameters are bilinear, and we prove its complexity is NP-hard even under simplifying assumptions. We consider a relaxation that provides an approximation, giving an overall guarantee of near-optimality when used with branch-and-bound search. We present preliminary computational experiments that illustrate the computational complexity of solving these robust formulations on sensor placement applications.

On the Integrality Gap of a Natural Formulation of the Single-Sink Buy-at-Bulk Network Design Problem

We study two versions of the single sink buy-at-bulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of flow to be routed to the sink. We are also given a finite set of cable types which have different cost characteristics and obey the principle of economies of scale. We wish to construct a minimum cost network to support the demands, using our given cable types. We study a natural integer program formulation of the problem, and show that its integrality gap is O(k), where k is the number of cable types. As a consequence, we also provide an O(k)-approximation algorithm.

Optimal-stretch name-independent compact routing in doubling metrics

We consider the problem of name-independent routing in doubling metrics. A doubling metric is a metric space whose doubling dimension is a constant, where the doubling dimension of a metric space is the least value α such that any ball of radius <i>r</i> can be covered by at most 2^α balls of radius <i>r</i>/2.Given any δ>0 and a weighted undirected network <i>G</i> whose shortest path metric <i>d</i> is a doubling metric with doubling dimension α, we present a name-independent routing scheme for <i>G</i> with (9+δ)-stretch, (2+1<over>δ)^O(α) (log δ)² (log <i>n</i>)-bit routing information at each node, and packet headers of size <i>O</i>(log <i>n</i>), where δ is the ratio of the largest to the smallest shortest path distance in <i>G</i>.In addition, we prove that for any ε ∈ (0,8), there is a doubling metric network <i>G</i> with <i>n</i> nodes, doubling dimension α ≤ 6 - log ε, and Δ=<i>O</i>(2^1/ε<i>n</i>) such that any name-independent routing scheme on <i>G</i> with routing information at each node of size <i>o</i>(<i>n</i>^(ε/60)²)-bits has stretch larger than 9-ε. Therefore assuming that Δ is bounded by a polynomial on <i>n</i>, our algorithm basically achieves optimal stretch for name-independent routing in doubling metrics with packet header size and routing information at each node both bounded by a polylogarithmic function of <i>n</i>.

Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems

We present simple semidefinite programming relaxations for the m-hard minimum bandwidth and minimum length linear ordering problems. We then show how these relaxations can be rounded in a natural way (via random projection) to obtain new approximation guarantees for both of these vertex-ordering problems.